On the palindromic and primitive widths of a free group.

DOI10.1016/j.jalgebra.2004.11.003zbMath1085.20011arXivmath/0311257OpenAlexW2057356537MaRDI QIDQ1772434

Vladimir Shpilrain, Vladimir Tolstykh, Valeriy G. Bardakov

Publication date: 18 April 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311257

zbMATH Keywords

free groupspalindromic widthsprimitive widths

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free nonabelian groups (20E05)

Related Items (21)

Palindromic widths of nilpotent and wreath products ⋮ Palindromic Width of Finitely Generated Solvable Groups ⋮ GENERATING GROUPS BY CONJUGATION-INVARIANT SETS ⋮ Palindromic primitives and palindromic bases in the free group of rank two. ⋮ Palindromic width of wreath products ⋮ On palindromic width of certain extensions and quotients of free nilpotent groups ⋮ Palindromic width of graph of groups ⋮ Unnamed Item ⋮ Primitive and almost primitive elements of Schreier varieties ⋮ 𝐴𝑢𝑡-invariant quasimorphisms on groups ⋮ Palindromic length of words and morphisms in class \(\mathcal{P}\) ⋮ On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus ⋮ Aut-invariant word norm on right-angled Artin and right-angled Coxeter groups ⋮ Enumerating palindromes and primitives in rank two free groups. ⋮ Palindromic width of free nilpotent groups. ⋮ Qualitative counting closed geodesics ⋮ Aut-invariant norms and Aut-invariant quasimorphisms on free and surface groups ⋮ Additive primitive length in relatively free algebras ⋮ Palindromes in the free metabelian Lie algebras ⋮ The palindromic width of a free product of groups ⋮ Palindromic words in simple groups

Cites Work

• What does a basis of F(a,b) look like?
• On generators of polynomial algebras in two commuting or non-commuting variables
• Geometry for palindromic automorphism groups of free groups
• Counting primitive elements in free groups
• A note on the automorphism group of the rank two free group
• A problem of expressibility in some amalgamated products of groups
• Bounded Elementary Generation of SL n (O)
• On the decomposition of automorphisms of free modules into simple factors
• The Automorphism Tower of a Free Group
• On Certain Sets of Elements in a Free Group
• On the width in free products with amalgamation
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